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Objectives: Curve simplification is of importance in automated map generalization; nevertheless, the Douglas-Peucker (DP) algorithm popularly used in map generalization is not automatic, because a key parameter called distance tolerance (ε) must be given by experienced cartographers and needs to be input before execution of the algorithm. Methods: To solve the problem, this paper proposed a method to automatically calculate ε and by which the automation of the DP algorithm is achieved. The method consists of the following steps: (1) A formula is constructed by the Hausdorff distance for calculating the similarity degree (Ssim) between a curve at a larger scale and its simplified counterpart at a smaller scale. (2) 15 linear rivers are selected, and each of them is manually simplified to get their counterparts at seven different scales. The Ssim of each original river and each of its simplified counterpart at a smaller scale can be obtained using the formula constructed by the Hausdorff distance, and 15×7=105 coordinate pairs consisting of (S,Ssim) can be got, and a function between Ssim and S are constructed by the curve fitting using the coordinates. (3) In the meanwhile, the 15 rivers are simplified using a number of ε, and the Ssim of each original river and each of its simplified counterpart at a smaller scale can be calculated using the formula constructed by the Hausdorff distance. In this way, a number of coordinate pairs (ε,Ssim) are got, and a function between ε and Ssim is constructed by the curve fitting. (4) By the function between Ssim and S and that between ε and Ssim, a formula between ε and S can be deducted. Using the formula ε can be calculated automatically, because in a map generalization task S is usually known. After this step, automation of the DP algorithm is achieved. Results: The experiment results show that (1) The proposed DP algorithm can automatically simplify the rivers in a specific geographical area to get the results at different scales; and (2) the resulting river curves generated by the proposed DP algorithm have a high degree of similarity with the ones made by experienced cartographers. Their average similarity degree is 0.927. Conclusion: The proposed DP algorithm can simplify curve features on maps automatically, and the results are highly intelligent and credible. Although only river data is tested in this paper, the principle of the proposed method can be extended to other linear features on maps. Our future work will be on improving the accuracy of the proposed DP algorithm using more river data so that the algorithm can be used in practical map generalization engineering. [ABSTRACT FROM AUTHOR]

Objectives: Most of the existing building simplification methods focus on one or two aspects of the three principles: Area preservation, shape characteristics enhancement and drawing rectangles if possible. In practice, map generalization is a process of mutual restriction and trade off of various influencing conditions, cartographic experts consider all the three aspects and balance them to reach reasonable results, sometimes they delete the small details on building's outlines, but it results in the area difference, sometimes they displace some points of the edges so that the area stays unchanged, but the vertices location changes. It depends on the short-edge structures and distributions. By imitating this thinking and operation process of cartographers, a method based on short-edge structure recognition and progressive simplification is proposed. Methods: Firstly, the building outline is preprocessed. Then the contour segments are grouped, and the edge structure is identified and analyzed. After this, some specific situations are analyzed in detail, and the calculation region (the sequence of vertices associated with the simplification of a set of edges less than the tolerance) is used to determine the optimal simplification method. Lastly, the area difference is distributed to the whole building so that the building's area difference is reduced while the shape is maintained. Open Street Map (OSM) buildings are selected in the experiment. Results: Experimental results show that the proposed method can effectively reduce the number of graphic vertices, enhances the shape characteristics like parallel, right angle, etc. Also, the approach can control the area differences after generalization. Conclusions: The proposed method gives consideration to three aspects of the building simplification principles and balances them, which provides a new way for building simplification. [ABSTRACT FROM AUTHOR]